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Decimal expansion of r = sum{[n/3]!/[n/2]!, n = 0..infinity} and [ ] = floor.
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%I #7 Oct 17 2014 23:21:22

%S 6,2,0,7,2,4,8,0,5,2,6,7,5,5,8,6,2,0,5,4,2,5,0,0,8,5,5,6,0,7,7,0,3,7,

%T 8,1,6,8,0,5,3,1,8,2,2,0,7,2,4,3,7,7,9,5,6,4,9,0,0,7,6,8,3,3,4,6,2,2,

%U 7,0,2,3,0,0,2,2,5,9,0,2,4,4,9,9,0,9

%N Decimal expansion of r = sum{[n/3]!/[n/2]!, n = 0..infinity} and [ ] = floor.

%H Clark Kimberling, <a href="/A248680/b248680.txt">Table of n, a(n) for n = 1..1000</a>

%e r = 6.207248052675586205425008556077037816805318220...

%t x = N[Sum[Floor[n/3]!/Floor[n/2]!, {n, 0, 400}], 120]

%t RealDigits[x][[1]] (* A248680 *)

%o (PARI) suminf(n=0, (n\3)!/(n\2)!) \\ _Michel Marcus_, Oct 17 2014

%Y Cf. A248679, A248681.

%K nonn,easy,cons

%O 1,1

%A _Clark Kimberling_, Oct 11 2014